To determine which statements are true regarding the perpendicularity of the given lines, we need to look at the slopes of each line from their equations.
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Line A: \(y = -12x - 2\)
- Slope (m) = -12
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Line B: \(y = 2x - 3\)
- Slope (m) = 2
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Line C: \(y = 12x + 2\)
- Slope (m) = 12
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Line D: \(y = 2x + 5\)
- Slope (m) = 2
Two lines are perpendicular if the product of their slopes equals -1.
Now we can evaluate the pairs given in the statements:
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Line A (slope -12) and Line B (slope 2): \[ -12 \times 2 = -24 \quad (\text{not perpendicular}) \]
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Line A (slope -12) and Line C (slope 12): \[ -12 \times 12 = -144 \quad (\text{not perpendicular}) \]
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Line B (slope 2) and Line D (slope 2): \[ 2 \times 2 = 4 \quad (\text{not perpendicular}) \]
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Line C (slope 12) and Line D (slope 2): \[ 12 \times 2 = 24 \quad (\text{not perpendicular}) \]
Since none of the pairs produce a product of -1, none of the statements about perpendicularity among the lines provided is true.
Therefore, all the statements provided are false.